Finite Group Databasebeta

← #16932006

Subgroups — #16932006

Order 4352.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537869C211yesmaximal, characteristic
2#14533769C211yesmaximal, characteristic
3#14527509C212yesmaximal
4#14526639C212yesmaximal
5C17×#1467C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×#10587630C412yes—
8#11762940—24no—
9#11762866—21no—
10#11762866C2212yes—
11#11762862—21no—
12#11762739—21no—
13#11762739—21no—
14#11762714C412yes—
15#11762707—21no—
16#11762707—21no—
17C4×C4⋊Dic17C2211yescharacteristic
18#11762557—24no—
19C2×C4×Q8×C17C2211yescharacteristic
20C17×#432C2212yes—
21C17×#324—21no—
22C17×#324—21no—
23C22×Q8×C17C2×C411yescharacteristic
24C22×Dic34C2×C412yes—
25C4×Q8×C17—22no—
26C4×Q8×C17—22no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33#10587630—44no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×#63225—22no—
38C2×#63225—22no—
39C2×C4×Dic17C2×C412yes—
40#10587555—22no—
41#10587555—22no—
42C17×C4⋊C8—22no—
43C17×C22⋊C8—22no—
44C17×#97—22no—
45#10587502—22no—
46#10587502—22no—
47#10587502—21no—
48C22⋊#3622—22no—
49C4⋊#3622—22no—
50C4⋊#3622—22no—
51C4⋊#3622D414yes—
52#10587474—22no—
53#10587474—22no—
54C4×#3622—22no—
55C2×Q8×C17—22no—
56C2×Q8×C17—22no—
57C2×Q8×C17—41no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C22×Dic17—22no—
66C22×Dic17—22no—
67C2×Dic34—24no—
68C2×Dic34—42no—
69C2×Dic34—42no—
70C2×C8×C17—42no—
71C4⋊C4×C17—22no—
72C4⋊C4×C17—22no—
73C4⋊C4×C17—22no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17C2×D412yes—
79C42×C17#4112yes—
80C4⋊Dic17—24no—
81C4⋊Dic17—41no—
82C4⋊Dic17—42no—
83C4⋊Dic17—41no—
84#63225—44no—
85#63225—44no—
86C4×Dic17—42no—
87C2×#3622—24no—
88#9452—171nomaximal, Sylow
89C23×C17C2×C22⋊C411yescharacteristic
90Q8×C17—44no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—22no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17#10012yes—
105C2×C4×C17C4×D412yes—
106C2×C4×C17#12011yescharacteristic
107C2×C4×C17#12112yes—
108C2×C4×C17#12311yescharacteristic
109C2×Dic17—24no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115Dic34—84no—
116C8×C17—82no—
117#3622—44no—
118#2983—171no—
119#2546—171no—
120#1558—172no—
121#1467D1711yescharacteristic
122#1285—172no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17#38611yescharacteristic
126C22×C17C2×#10011yescharacteristic
127C22×C17#41311yescharacteristic
128C4×C17—21no—
129C4×C17—22no—
130C4×C17—22no—
131C4×C17—22no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17#45612yes—
136Dic17—44no—
137Dic17—82no—
138C2×C4⋊Q8—172no—
139C2×C4⋊Q8—171no—
140C2×C4×Q8C2×D1711yescharacteristic
141#446—344no—
142#432—172no—
143#432—341no—
144#432C2×D1712yes—
145#431—341no—
146#398—341no—
147#398—341no—
148#391—172no—
149#389—341no—
150#389—341no—
151C4×C4⋊C4—171no—
152#333—344no—
153#324—21no—
154#324—21no—
155C2×C17—21no—
156C2×C17—21no—
157C2×C17#188611yescharacteristic
158C2×C17#190011yescharacteristic
159C2×C17#190911yescharacteristic
160C22×Q8—172no—
161C22×Q8C4×D1711yescharacteristic
162C4⋊Q8—342no—
163C4⋊Q8—342no—
164C4⋊Q8—684no—
165C4×Q8—22no—
166C4×Q8—22no—
167C2×C4⋊C4—341no—
168C2×C4⋊C4—341no—
169C2×C4⋊C4—341no—
170C2×C4⋊C4—342no—
171C2×C4⋊C4—342no—
172C2×C4⋊C4C4×D1711yescharacteristic
173C2×C4⋊C4C22⋊D1711yescharacteristic
174C2×C4⋊C4C22⋊D1711yescharacteristic
175C2×C42—172no—
176C2×C42D6811yescharacteristic
177C2×C42D6811yescharacteristic
178C2×C42C22×D1711yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—174no—
181C4⋊C8—342no—
182C4⋊C8—342no—
183C22⋊C8—22no—
184C22⋊C8—342no—
185#97—22no—
186#97—342no—
187#97—342no—
188C4×C8—342no—
189#95—341no—
190#95—342no—
191#95—342no—
192C17#945211yescharacteristic, complemented, Sylow
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—344no—
197C2×Q8—682no—
198C2×Q8—682no—
199C22×C4—342no—
200C22×C4—342no—
201C22×C4#6322711yescharacteristic
202C22×C4#6322711yescharacteristic
203C22×C4#6322711yescharacteristic
204C22×C4#6322711yescharacteristic
205C22×C4C2×C4×D1711yescharacteristic
206C22×C4C2×D6811yescharacteristic
207C22×C4C2×C22⋊D1711yescharacteristic
208C2×C8—42no—
209C2×C8—344no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—344no—
214C4⋊C4—684no—
215C4⋊C4—684no—
216C4⋊C4—681no—
217C4⋊C4—681no—
218C4⋊C4—682no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—682no—
224C42D4×D1712yes—
225C42#6325412yes—
226C23C2×#6322711yescharacteristic
227Q8—44no—
228Q8—1364no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—344no—
243C2×C4—682no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4#1058749412yes—
249C2×C4#1058756712yes—
250C2×C4#1058756811yescharacteristic
251C2×C4#1058757211yescharacteristic
252C2×C4#1058762512yes—
253C8—82no—
254C8—684no—
255C22—21no—
256C22—21no—
257C22#1176268611yescharacteristic
258C22C2×#1058749411yescharacteristic
259C22#1176279111yescharacteristic
260C4—22no—
261C4—21no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—684no—
268C4—1362no—
269C4#1176299412yes—
270C2—21no—
271C2—21no—
272C2#1452917511yescharacteristic
273C2#1452924511yescharacteristic
274C2#1452930411yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1467C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1467D17
hypocenterC17#9452
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
192. C17#9452semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145378692
#145337692
#145275092
#145266392
C17×#14672
#945217